What is the general solution for arctan(x)= pi/3 ?

The general solution for arctan(x)= pi/3 is x=sqrt(3)

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arctan(x)= pi/3

arctan (x) = \frac{π}{3}

x = 3

Solution steps

arctan (x) = \frac{π}{3}

Apply trig inverse properties

arctan (x) = \frac{π}{3}

arctan (x) = a \Rightarrow x = tan (a)

x = tan (\frac{π}{3})

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= 3

x = 3

x = 3

2 cos (2 x) - 2 sin (x) = 0

cos (2 x) + 3 cos (x) - 1 = 0

cos (2 θ) = - 1

2 sin^{2} (x) - 1 = sin (x)

4 csc^{2} (θ) - 9 = 0

What is the general solution for arctan(x)= pi/3 ?
The general solution for arctan(x)= pi/3 is x=sqrt(3)